Answer:
See below.
Step-by-step explanation:
This inequality is < 0 for all real values of x. We see this by solving -x^2 - 6 = 0 for x:
-x^2 - 6 = 0
-x^2 = 6
x^2 = -6 for which there are no real solutions of x. So the graph does not pass through the x axis.
At x = 0. f(x) < -6 so that is the one critical value - all values of f(x) are below this value.
Answer:
0 critical points
Step-by-step explanation:
Just did it and got it right
A rectangular prism is 11 3/5 meters long 9 meters wide and 12 1/2 meters high what is the volume in cubic meters?
Answer:
7569 meters cubed
Step-by-step explanation:
first: make the improper fractions to a fraction greater than one.
11 3/5= 58/5
12 1/2 = 145/2
9=9
then you have to multiply them all together
cross multiply 58/5 and 145/2...you should get 841. Now multiply 841 and 9...you should get 7569 meters cubed.
*When VOLUME of a RECTANGLE is given, make sure to MULTIPLY the HIEGHT, WIDTH and the LEGNTH.
v=lwhAnswer:
7569³m
Step-by-step explanation:
1) The graph shows a probability distribution.
What is P(X<5)?
A) 0.3
B) 0.375
C) 0.625
D) 0.7
2) The graph shows a probability distribution.
Which probabilities are equal to 0.2?
Select each correct answer.
1) P(X≤2)
2) P(X≥4)
3) P(2≤X≤4)
4) P(1≤X≤3)
1. [tex]P(X<5)[/tex] is the area under the curve to the left of [tex]x=5[/tex], which is a trapezoid with "bases" of length 2 and 5 and "height" 0.2, so
[tex]P(X<5)=\dfrac{5+2}2\cdot0.2=0.7[/tex]
2. Find the area under the curve for each of the specified intervals:
[tex]P(X\le2)=\dfrac{2\cdot0.2}2=0.2[/tex] (triangle with base 2 and height 0.2)
[tex]P(X\ge4)=\dfrac{1\cdot0.4}2=0.2[/tex] (triangle with base 1 and height 0.4)
[tex]P(2\le X\le4)=\dfrac{0.2+0.4}2\cdot2=0.6[/tex] (trapezoid with "bases" 0.2 and 0.4 and "height" 2)
[tex]P(1\le X\le3)=\dfrac{0.1+0.3}2\cdot2=0.4[/tex] (trapezoid with "bases" 0.1 and 0.3 and "height" 2)
The required probabilities are found using the given graphs of the
probability distributions.
Response:
1) P(X< 5) is D) 0.7
2) The probability equal to 0.2 are;
P(X ≤ 2)P(X ≥ 4)How can the probabilities be calculated from the graph of a probability distribution?The probabilities are given by the area under the curve of the graph of
the probability distribution, which are found as follows;
1) The given figure is a trapezium, which gives;
[tex]Area \ of \ a \ trapezium = \mathbf{\dfrac{a + b}{2} \cdot h}[/tex]
Where;
a, and b are the parallel sides of the trapezium
h = The height
Therefore;
[tex]P(X < 5) = \dfrac{5 + 2}{2} \times 0.2 = \mathbf{0.7}[/tex]
P(X< 5) = D) 0.72) The probabilities equal to 0.2 are found as follows;
1) At P(X ≤ 2), the area is a triangle, which gives;
[tex]Area \ of \ a \ triangle = \mathbf{\dfrac{1}{2} \times Base \ length \times Height\sqrt{x}}[/tex]
[tex]P(X \leq 2) = \dfrac{1}{2} \times 2 \times 0.2 = \mathbf{0.2}[/tex]
P(X ≤ 2) = 0.22) At P(X ≥ 4), has a triangular area, which gives;
[tex]P(X \geq 4) = \mathbf{\dfrac{1}{2} \times 1 \times 0.4}= 0.2[/tex]
P(X ≥ 4) = 0.23) P(2 ≤ X ≤4) has a trapezoidal area, which gives;
[tex]P( 2 \leq X \leq 5) = \mathbf{\dfrac{0.2 + 0.4}{2}} \times 0.2 = 0.6[/tex]
P(2 ≤ X ≤4) = 0.6 ≠ 0.2
4) P(1 ≤ X ≤ 3) has a trapezoidal area, which gives;
[tex]P( 1 \leq X \leq 3) = \dfrac{0.1 + 0.3}{2} \times 2 = 0.4[/tex]
P(1 ≤ X ≤ 3) = 0.4 ≠ 0.2
Therefore;
The probabilities that are equal to 0.2 are;
P(X ≤ 2) = 0.2P(X ≥ 4) = 0.2Learn more about probability distributions here:
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On Friday John has $100 over the weekend he bought pizza for $37 and uses his debit card for concert tickets that cost $89 how much money did John have on Monday
Final answer:
After spending $37 on pizza and $89 on concert tickets, John overdrawn his account by $26. This calculation subtracts the total expenses from his initial amount, resulting in a negative balance.
Explanation:
John initially has $100, and we need to calculate how much money he will have on Monday after his expenses over the weekend. He bought pizza for $37 and concert tickets for $89, totaling $126 in expenses. To find out how much money John has left, we subtract his total expenses from his initial amount:
Initial Amount: $100
Total Expenses (Pizza + Concert Tickets): $37 + $89 = $126
Now, subtract the total expenses from the initial amount:
$100 - $126 = -$26
This means John will have a deficit of $26. Since he spent more than what he initially had, it implies he has overdrawn his account by $26.
Heather and her lab partners were trying to find the probability that the weight of a US quarter is below one standard deviation from the mean. They know that the weight of a quarter follows the normal distribution. What was their answer?
Answer:
16%
Step-by-step explanation:
The Empirical rule says that 68% of a normal distribution lies between -1 and +1 standard deviations.
That means that 32% lies outside of ±1 standard deviations.
Since the normal curve is symmetrical, that means 16% is less than -1 standard deviation and 16% is greater than +1 standard deviation.
So the answer is 16%.
Heather and her lab partners found that the probability of the weight of a US quarter being below one standard deviation from the mean is 16%.
Heather and her lab partners need to find the probability that the weight of a US quarter is below one standard deviation from the mean. Since the weight of a quarter follows a normal distribution, we use the property of the normal distribution to find this probability.
In a normal distribution:
Approximately 68% of the data lies within one standard deviation (σ) of the mean (μ).This implies that roughly 34% of the data is between the mean and one standard deviation below the mean, and another 34% between the mean and one standard deviation above the mean.Therefore, the probability of a weight being below one standard deviation from the mean is 16%. This is calculated by taking half of the remaining probability outside the 68%, which is (100% - 68%) ÷ 2 = 16%.
the cone and the cylinder below have equal surface area. True or false.
Answer:
False
Step-by-step explanation:
The surface area of the cone is
[tex]V=\pi r^2 +\pi rl[/tex]
[tex]SA=\pi r^2 +\pi\times r\times 2r[/tex]
[tex]SA=\pi r^2 +2\pi\times r^2[/tex]
[tex]SA=3\pi r^2[/tex]
The surface area of the cylinder is:
[tex]SA=2\pi r^2 +2\pi rh[/tex]
[tex]SA=2\pi r^2 +2\pi\times r\times r[/tex]
[tex]SA=4\pi r^2 [/tex]
An animal shelter spends $5.00 per day to care for each bird and $8.50 per day to care for each cat. Nicole noticed that the shelter spent $132.50 caring for birds and cats on Tuesday. Nicole found a record showing that there were a total of 23 birds and cats on Tuesday. How many birds were at the shelter on Tuesday?
Answer:
the answer is 18 birds and 5 cats
Step-by-step explanation:
the easiest way i did this was that i used a calculator and kept subtracting 8.5 untill i reached a number that was completely divisable by 5, i subtracted 8.5 five times which got the total down to 90$ and since each bird is 5$ you can just divide which means there was a total of 18 bird and 5 cats on Tuesday
To find out how many birds were at the shelter on Tuesday, we set up and solved a system of linear equations involving the total daily care costs and the total number of animals. By substituting and simplifying, we found the number of birds among the 23 animals.
The question involves solving a system of linear equations to find out how many birds were at the shelter on Tuesday, given the daily care costs for birds and cats, the total cost for Tuesday, and the total number of birds and cats. We use the information that the shelter spends $5.00 per day to care for each bird and $8.50 per day to care for each cat, with a total expenditure of $132.50 for 23 birds and cats together.
Let x be the number of birds and y be the number of cats. Therefore, we have two equations:
5x + 8.5y = 132.50x + y = 23From the second equation, we can isolate one variable, say x = 23 - y. Substituting this into the first equation gives us:
5(23 - y) + 8.5y = 132.50
After simplifying, we find the value of y, and then substitute back to find x, which represents the number of birds. This method of solving the system of equations is straightforward and efficient for this problem.
Bob ran 5 1/4 miles at a pace of 3 3/8 miles per hour.How long was he running in hours.
Answer:
1 5/9
hope it helped
Step-by-step
divide 5 1/4 by 3 3/8 to get 1 5/9
Can someone explain this to me.
Answer:
option D
[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]
Step-by-step explanation:
Given in the question an expression,
[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}[/tex]
Step 1
Divide and multiple by [tex]\sqrt{x}+\sqrt{x-3}[/tex] to remove radical sign from denominator.
[tex]\frac{9}{\sqrt{x} -\sqrt{x-3}}*\frac{\sqrt{x} +\sqrt{x-3}}{\sqrt{x} +\sqrt{x-3}}[/tex]
Step 2
Apply a² - b² = (a+b)(a-b)
[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{\sqrt{x^{2}}-\sqrt{(x-3)^{2}}}}[/tex]
Step 3
[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{x-x+3}[/tex]
Step 4
[tex]\frac{9*\sqrt{x}+\sqrt{x-3}}{3}[/tex]
Step 5
[tex]3*(\sqrt{x}+\sqrt{x-3})[/tex]
No specific question was provided. Therefore, a clear question related to a specific subject and grade needs to be put forward for a detailed, example-filled explanation.
Explanation:Since there is no specific question provided, it is not possible to provide an accurate and factual answer. Therefore, in order to give a comprehensive answer, a clear and specific question related to a given subject like Mathematics, History, English, Biology, Chemistry, Physics, etc., and grade (Middle School, High School, College) needs to be provided. Once the question is presented, I would be delighted to provide a detailed explanation, using relevant examples and details to help you understand the concept.
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Find the median of each set of data. 12, 8, 6, 4, 10, 1 6, 3, 5, 11, 2, 9, 5, 0 30, 16, 49, 25
Answer:
7
5
27.5
Step-by-step explanation:
edgu 2020
Answer:first 7 then 5 and 27.5 used the other person and got it right on edge:)
Step-by-step explanation:
I am hoping someone could kindly show the step by step instruction to solve this equation. I have tried to solve it many times but it is still not clear, could someone please show the steps 2(8r^2+r)-4r Thanks
Answer: 30r
Step-by-step explanation:
2(8r2+r)-4r
2(17r)-4r
34r-4r
30r
Answer:
16r^2-2r
Step-by-step explanation:
2(8r^2+r)-4r
(16r^2 +2r)-4r Distribute the 2
16r^2+(2r-4r) Regroup like terms
16r^2-2r
Hope this helps!
The yellow dog is smaller than the brown dog but larger than the white dog. The black dog is smaller than the white dog and the yellow dog. Which dog is the smallest?
Answer:
Black
Step-by-step explanation:
Black-White-Yellow-Brown
Also can you please rate this as the most brainliest because I need it to level up?
Please help !!!!!!!!!!!
Answer:
x = 58.0
Step-by-step explanation:
We can use the inverse of cos to solve for x once you set up the equation
[tex]cosx = \frac{9}{17}[/tex]
This is as 9 is the adjacent side and 17 is the hypotenuse of the triangle.
We can then solve for x using the inverse of cos
[tex]x= cos^{-1} (\frac{9}{17} )[/tex]
When plugged into a calculator you get
x= 58.03 degrees
this rounds to 58.0 degrees
NEED HELP PLS!!!!!!!!!!!! BRANLIEST+15 POINTS!
A rectangle has a width that is 3 less than twice the length. If the rectangle has an area of 170 square inches, what is the length of the rectangle?
Answer:
L = 10, w = 17
Step-by-step explanation:
Area of a rectangle is A = Lw. We are told that the width is 3 less than twice the length, so we will change the width into some expression in terms of the length.
w = 2L - 3 and
length = L.
Filling in the area formula now, knowing that the area is given as 170:
170 = (2L - 3)(L) so
[tex]170=2L^2-3L[/tex]
Get everything on one side of the equals sign and throw it into the quadratic formula to factor it and solve for the values of L. When we do this we get that L = 10 and L = -8.5
Since the 2 things in math that will NEVER EVER be negative are time and distance/length measures, it is safe to disregard the -8.5. Therefore,
if L = 10, then
w = 2(10) - 3 and
w = 17
HELP PLEASE! In ΔABC, m∠A = 43°, m∠B = 62°, and BC = 22 in. What is AB to the nearest tenth of an inch?
28.5 in.
15.6 in.
14.1 in.
31.2 in.
The length AB of the triangle is 31.2 inches.
How to find the side of a triangle?The side AB of the triangle can be found using sine rule for triangles as follows:
Using sine law,
a / sin A = b / sin B = c / sin C
Hence,
22 / sin 43 = AB / sin 75
cross multiply
AB sin 43 = 22 sin 75
divide both sides by sin 43
AB = 22 sin 75 / sin 43
AB = 21.2503681784 / 0.68199836006
AB = 31.1629271154
AB = 31.2 inches
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The two square pyramids are similar. The side length of the smaller pyramid is 3/4 the side length of the larger pyramid.Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid? A.9/16 B.3/4 C.4/3 D.16/9
Answer:
The side length of the smaller pyramid is 3/4 the side length of the larger pyramid.
Step-by-step explanation:
Snow Crest is 11,990.21 feet higher than Mt. Wilson. Write and solve an equation to find the elevation of Mt. Wilson. Let x represent the elevation of Mt. Wilson.
Answer:
The elevation of Mt. Wilson is 16,160.10 ft
Step-by-step explanation:
Let
x-----> represent the elevation of Mt. Wilson
y ----> represent the elevation of Snow Crest
we know that
y=x+11,990.21 ----> linear equation that represent this situation
we have that
y=28,150.31 ft ----> see the attached figure
substitute in the linear equation and solve for x
28,150.31=x+11,990.21
x=28,150.31-11,990.21=16,160.10 ft
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = quantity x minus nine divided by quantity x plus five. and g(x) = quantity negative five x minus nine divided by quantity x minus one.
Show work pls
ANSWER
See below
EXPLANATION
Given
[tex]f(x) = \frac{ {x}- 9 }{x + 5} [/tex]
and
[tex]g(x) = \frac{ - 5x - 9}{x - 1} [/tex]
[tex](f \circ \: g)(x)= \frac{ (\frac{ - 5x - 9}{x - 1})- 9 }{(\frac{ - 5x - 9}{x - 1} )+ 5} [/tex]
[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9(x - 1)}{x - 1}}{\frac{ - 5x - 9 + 5(x - 1)}{x - 1} } [/tex]
Expand:
[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9 - 9x + 9}{x - 1}}{\frac{ - 5x - 9 + 5x - 5}{x - 1} } [/tex]
[tex](f \circ \: g)(x)= \frac{ \frac{ - 5x - 9x + 9 - 9}{x - 1}}{\frac{ - 5x + 5x - 5 - 9}{x - 1} } [/tex]
[tex](f \circ \: g)(x)= \frac{ \frac{ - 14x }{x - 1}}{\frac{ -14}{x - 1} } [/tex]
Since the denominators are the same, they will cancel out,
[tex](f \circ \: g)(x)= \frac{ - 14x}{ - 14} = x[/tex]
The volume in cubic feet of a box can be expressed as (x) = x^3 - 6x^2 + 8x , or as the product of three linear factors with integer coefficients. The width of the box is x-2. Factor the polynomial to find linear expressions for the height and the length. Show your work.
Answer:
Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.
Step-by-step explanation:
The volume is given in terms of x as [tex]V(x)=x^3-6x^2+8x[/tex].
We factor the GCF to get;
[tex]V(x)=x(x^2-6x+8)[/tex].
We split the middle term of the trinomial in the parenthesis.
[tex]V(x)=x(x^2-4x-2x+8)[/tex].
We now factor the expression within the parenthesis by grouping;
[tex]V(x)=x[x(x-4)-2(x-4)][/tex].
[tex]V(x)=x(x-2)(x-4)[/tex].
Since the width of the box is [tex]x-2[/tex] units, the linear expression for the height and length is [tex]x(x-4)[/tex]
Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.
Vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units. Which of these values are possible for the magnitude of u + v? Select all correct answers.
1 unit
9 units
11 units
13 units
Step-by-step answer:
The maximum and minimum values are the positive sum and difference of the two magnitudes. The magnitude of u+v can range between these two limits, namely 5+4=9, and 5-4=1.
Therefore among the given choices, the possible values of u+v are 1 unit and 9 units. 11 and 13 are greater than the maximum so do not apply.
Answer:
1 unit
9 units
Step-by-step explanation:
PLATO
Hi please please help me
Answer:
141.12 cm^2
Step-by-step explanation:
Since the area of a trapezoid is the average of the bases multiplied by the height, we can just plug these numbers into the equation! Since the average of 10.2 and 12.2 is 11.2, and the height is 12.6, we multiply them to get the area to be 141.12 cm^2.
Answer:
141.12cm^2
Step-by-step explanation:
I do not know if this is the correct way to do it, but I split the trapezoid in half, then putting it on top of each other to create a rectangle, which is (10.2cm+12.2cm)(12.6cm/2)
Identify the surface area of the composite figure to the nearest tenth. PLEASE HELP!!
1666.1 cm^2
1553.0 cm^2
1923.0 cm^2
Answer:
1553 cm^2.
Step-by-step explanation:
Surface area of the top part = area of the lateral part of the cylinder + area of the top circle
= 2π*6*10 + π*6^2 = 490.09 cm^2
Surface area of the bottom part
= surface area of the cube - surface area of the bottom of the cylinder
= 6 * 14^2 - π*6^2 = 1062.90
Total surface area = 490.09 + 1062.90 = 1553 cm^2.
In the system shown below, what are the coordinates of the solution that lies in quadrant I?
Write your answer in the form (a,b) without using spaces.
[tex]x^{2} +y^2=25[/tex]
[tex]x-y^2=-5[/tex]
Answer:
(4,3)
Step-by-step explanation:
Given
x^2+y^2=25
x-y^2=-5
In order to solve the equations, from equation 2 we get
-y^2= -5-x
y^2=5+x
Putting the value of y^2 in equation 1
x^2+5+x=25
x^2+5-25+x=0
x^2+x-20=0
x^2+5x-4x-20= 0
x(x+5)-4(x+5)=0
(x+5)(x-4)=0
So
x+5=0 x-4=0
x=-5 x=4
Now for x=-5
x^2+y^2=25
(-5)^2+y^2=25
25+y^2=25
y^2=25-25
y^2=0
so Y=0
And for x = 4
x^2+y^2=25
(4)^2+y^2=25
16+y^2=25
y^2=25-16
y^2=9
y= ±3
So the solution to the system of equations is
(-5,0) , (4,3), (4,-3)
The only solution that belongs to first quadrant is (4,3)
Answer:
(4,3)
Step-by-step explanation:
solve the simultaneous equations
x²+y²=25.........................(i)
x-y²= -5.............................(ii) ⇒make y² the subject of the equation;
y²=x+5.................................(iii)
Substitute equation (iii) in (i)
x² + x+5 =25
x²+x=25-5
x²+x-20=0..........solve for the quadratic equation
x(x-4)+5(x-4)=0
(x-4)(x+5)=0
x-4=0
x= 4 or
x+5=0
x= -5
finding value of y
if y²=x+5 then;
when x=4, y²=4+5=9⇒y=√9 = ±3...................y= ±3
when x= -5 , y²= -5+ 5=0............... y=0
Coordinates = (4,3) and (-5,0)
Coordinates that lie in the 1st quadrant is (4,3)
A classroom is made up of 11 boys and 14 girls. The teacher has four main classroom responsibilities that she wants to hand out to four different students (one for each of the four students). If the teacher chooses 4 of the students at random, then what is the probability that the four students chosen to complete the responsibilities will be all boys?
Final answer:
The probability of choosing all boys for the classroom responsibilities from a classroom of 11 boys and 14 girls is calculated using combinatorial probability, which is the ratio of the number of ways to choose 4 boys out of 11 to the total number of ways to choose 4 students out of 25.
Explanation:
The probability that all four students chosen at random from a classroom of 11 boys and 14 girls will be boys is a classic example of a combinatorial probability question.
First, we calculate the total number of ways to choose 4 out of 25 students, which is the combination of 25 students taken 4 at a time. This is given by the binomial coefficient 25 choose 4, which is calculated as 25! / (4! * (25-4)!).
Next, we calculate the total ways to choose 4 out of the 11 boys, which is the combination of 11 boys taken 4 at a time, given by 11 choose 4, calculated as 11! / (4! * (11-4)!).
The probability is the ratio of the number of favorable outcomes (only boys chosen) to the total number of outcomes. Therefore, the probability is (11 choose 4) / (25 choose 4).
What is the perimeter of a right triangle whose hypotenuse is the line segment A(-7, 5) B(1,0)
Answer:
it depends
Step-by-step explanation:
The endpoints of the hypotenuse are insufficient to specify a right triangle. The perimeter can range from twice the distance between these points, about 18.868 units, to 1+√2 times the distance between these points, about 22.776 units.
___
In the attached figure, the colored numbers are the total length of the two legs of that color. The hypotenuse and its length are in black.
_____
The distance between two points is given by the formula ...
d = √((x2-x1)^2 +(y2 -y1)^2)
The perimeter will be the sum of the distances between pairs of points that define the vertices of the triangle. We need to know the third vertex to answer the question precisely.
What is the solution to the system of equations?
2x−y+z=−8
x+y+z=−4
3x−y−z=−4
Answer:
The solution to this system is (-2, 1, -3).
Step-by-step explanation:
Let's eliminate variable x first. Combine the first two equations, obtaining:
3x - 0y + 2z = -12.
Now subtract the third equation from this result:
3x - 0y + 2z = -12
-(3x − y − z = −4)
----------------------------
y + 3z = -8
Similarly, combine the second and third original equations to eliminate x again. To do this, subtract 2(x + y + z = -4) from the first equation:
2x−y+z=−8
-2x - 2y - 2z = 8
-----------------------
-3y - z = 0
Now we have eliminated x completely, and find from -3y - z = 0 that z = -3y. Substitute this -3y for z in the equation y + 3z = -8 found above:
y + 3(-3y) = -8. Then y - 9y = -8, and so y must = 1. From -3y - z = 0, substituting 1 for y, we find that z = -3(1), or z = -3.
Finally, subst. 1 for y and -3 for z in the second equation:
x + 1 - 3 = -4
So, x - 2 = -4, and thus x must be -2.
The solution to this system is (-2, 1, -3).
A square rug covers 79 square feet of floor. What is the approximate length of one side of the rug? (Approximate to the nearest hundredth foot.) 8.86 feet. 8.87 feet. 8.88 feet. 8.89 feet.
Answer:
8.89 feet
Step-by-step explanation:
The square of the side length is 79 ft², so the side length is the square root of that:
√(79 ft²) ≈ 8.88819 ft ≈ 8.89 ft
The circle below is centred at point (2,-1) and has a radius of length 3 what is its equation ?
Apex
Answer:
Option C
Step-by-step explanation:
The standard form of equation of a cirle is:
(x-h)^2+ (y-k)^2=r^2
In the given question as the point is given and the radius of circle is given:
So,
(h,k)=(2,-1)
and
r=3
Here,
h=2
k= -1
Putting the values of h,k and r in standard form
(x-2)^2+ (y-(-1))^2=(3)^2
(x-2)^2+ (y+1)^2=(3)^2
So the equation of circle is:
(x-2)^2+ (y+1)^2=9(3)^2
Option C is the correct answer ..
The extended warranty on a $960 dishwasher is 21% of the purchase price and lasts for eight years. What is the effective cost per year of the extended warranty?
Answer:
$25.20
Step-by-step explanation:
Find 21% of $960
.21*960=201.6
Since there are 8 years, the cost per year will be the total cost divided by 8.
201.6/8=25.2
The cost per year is $25.20 on the extended warranty.
Answer:
50
Step-by-step explanation:
Valeria drives 500 meters up a hill that makes an angle of 15 degrees with the horizontal. To the nearest tenth of a meter, what horizontal distance has she covered?
Answer:
Approximately 485 meters
Step-by-step explanation:
We can first construct a right triangle, using the 500 m length of hill as our hypotenuse. Using the fact that the cosine of an angle is the ratio of the adjacent side to the hypotenuse, we see that
[tex]\cos{15^\circ}=\frac{x}{500}[/tex]
where x is the horizontal distance covered. Solving for x, we find this horizontal distance to be
[tex]x=500\cos{15^\circ}\approx500(0.97)=485[/tex]
so our answer is approximately 485 m.
The red stripe on a barber pole makes two complete revolutions around the pole. The pole is 260 cm high, and 14 cm in diameter. How long is the stripe? What angle does it make with the horizon?
Answer:
[tex]\boxed{\text{274.5 cm; }71.3^{\circ}}[/tex]
Step-by-step explanation:
If we open the surface of the pole and lay it flat, we will get a rectangle with the red stripe as a diagonal.
l = 260 cm.
The width of the rectangle is enough for two revolutions (i.e., twice the circumference).
w = 2C = 2 × 2πr = 4π × 14/2 = 28π cm = 87.96 cm
Length of stripe
The stripe is the diagonal of the rectangle.
d² = 260² + (28π)² = 67 600 + 87.96² = 67 600 + 7738 = 75 338
d = √(75 338) = 274.5 cm
Angle with horizontal
tanθ = 260/(28π) = 260/87.96 =2.956
θ = arctan2.956
θ = 71.3°
The stripe is [tex]\boxed{ \text{274.5 cm}}[/tex] long and the angle with the horizontal is [tex]\boxed{71.3^{\circ}}[/tex].
Final answer:
The red stripe on the barber pole is approximately 520.8 cm long and makes an angle of about 71.1 degrees with the horizon.
Explanation:
The problem describes a cylinder (barber pole) with a helical stripe wrapping around it. To find the length of the stripe, we need to construct a right-angled triangle by unwrapping the helix. One side of the triangle is the height of the pole (260 cm), and the other side is the circumference of the pole multiplied by the number of revolutions (2).
First, calculate the circumference using the diameter given:
Circumference = π × diameter = 3.1416 × 14 cm ≈ 44 cmThe length of the stripe is then the hypotenuse of the right triangle, which can be found using the Pythagorean theorem:
Hypotenuse² = Height² + (Circumference × Revolutions)²Hypotenuse = √(2602 + (44 × 2)²)Hypotenuse ≈ 520.8 cmFor the angle with the horizon, θ, we use the tangent function:
tan(θ) = opposite/adjacent = Height / (Circumference × Revolutions)θ = arctan(Height / (Circumference × 2))θ = arctan(260 / 88) ≈ 71.1°The angle with the horizon is approximately 71.1 degrees. So, the length of the stripe is about 520.8 cm, and it makes an angle of roughly 71.1° with the horizon.